Kolisch



1955 E. KOLISCH EQUIPMENT FOR PROMOTING ECONOMICAL AND SAFE LOADING OFAIRCRAFT Original Filed Feb. 26, 1952 5 Sheets-Sheet 1 INVENTQR Ema]Kolz'sch B flaw w AM ATTORNEYS Re. 23,945 G ECONOMICAL AND'SAFE LOADINGOF AIRCRAFT Original Filed Feb. 26, 1952 Feb. 15, 1955 E. KOLISCHEQUIPMENT FOR PROMOTIN 5 Sheets-Sheet 2 INVENTOR EmzZ KoZzsck ATTORNEYSE. KOLISCH 23,945 EQUIPMENT FOR PROMOTING ECONOMICAL AND SAFE LOADING OFAIRCRAFT 5 Sheets-Sheet 5 INVENTQR Ema? Kolasch F/ZMAJ M ATTORNEYS Illwas

AYRQM Feb. 15, 1955 Original Filed Feb. 26, 1952 mum \Sm mum mum g mm E.KOLISCH EQUIPMENT FOR PROMOTING Feb. 15, 1955 5 Sheets-Sheet 4 A s WM mMm m W mmm MM MM JLIAQJLQM Q kw 5 5} QM J. I; g .1 3w w 1% km W a @iig ia fi ML? www wi i T w m .QQ kw QM E H mm W www E gm mm wmwwwfl L N i QR@m EFT. qwmi wmw 5 5 3 i \mQ \QQ RQ 5 G g m Wow w 5E4 @w Em Ev NE Rm mmEm Feb. 15, 1955 E. KOLISCH EQUIPMENT FOR PROMOTING ECONOMICAL AND SAFELOADING OF AIRCRAFT Original Filed. Feb. 26, 1952 5 Sheets-Sheet 5Ill/ll/ f//A///////////// ////////////lfl/l/l/l/ll/l/I/ INVENTOR Emu?Kvlzlsciz/ BY 1 624%. A'ITORNEYS United States Patent EQUIPMENT FORPROMOTING ECONOMICAL AND SAFE LOADING OF AIRCRAFT Emil Kolisch, NewYork, N. Y., assignor to Continental Silver Co. Inc., Brooklyn, N. Y., acorporation of New York Original No. 2,686,634, dated August 17, 1954,Serial No. 273,493, February 26, 1952. Application for reissue November26, 1954, Serial No. 471,548

16 Claims. (Cl. 235-61) Matter enclosed in heavy brackets II] appears inthe original patent but forms no part of this reissue specification;matter printed in italics indicates the additions made by reissue.

As conducive to an understanding or the invention, it is noted that inorder for an aircraft to take off, fly and land safely, its center ofgravity along the length of the plane must be at some predeterminedlocation which may vary between certain definite fixed limits.

These permissible fixed limits are determined by the manufacturer of theaircraft, ordinarily by flight tests, and are generally expressed withrespect to the mean aerodynamic chord, hereinafter designated MAC. TheMAC of an aircraft is described in text books as the chord of anair-foil, which is generally a definite segment between the leading andtrailing edges of the wing.

The distance of the center of gravity of an aircraft from a fixedreference datum is equal to the total moment of such aircraft about suchreference datum divided by its total weight. Where the nose of theaircraft is selected as the reference datum, and the aircraft is of thetype having a nose wheel and a pair of main wheels, the distance of eachwheel from the nose along the length or longitudinal axis of theaircraft is multiplied by the weight on the corresponding wheel todetermine the respective moments about the nose. The sum of thesemoments is divided by the sum of the three weights to determine thedistance of the center of gravity from the nose.

Such calculations may be expressed by the formula:

ICC

To illustrate the two formulas above-mentioned, let it be assumed thatthe nose wheel of an aircraft is 100 inches from its nose and carries aweight of 10,000 pounds and the two main wheels are 430 inches from thenose and each carries a weight of 30,000 pounds.

In the first formula we find:

In the second formula for CG, we

As the center of gravity determined by the first formula utilized thenose of the aircraft as the reference datum, the value determined, i.e., 382.86 inches, is the distance of the center of gravity from thenose. In the second formula the main wheels were used as the referencedatum and the value of 47.14 inches in the direction of the nose Wheelis the distance of the center of gravity from the main wheels. As thedistance from the nose of the aircraft to the main wheels is equal to430 inches, it is apparent that regardless of which formula is used, thecenter of gravity will be at the same location, i. e., 382.86 inchesfrom the nose of the aircraft;

Assuming that the aircraft, after the center of gravity has beendetermined, as above described, is loaded with an additional weight of1,000 pounds at a point 200 inches from its nose, the new center ofgravity as thus loaded may be determined by the following formula:

(CG Xweight) (added weight Xarm) The center of gravity may be determinedmore simply by using the main wheels as the reference datum. Thequotient of the product of weight on the nose wheel by its distance fromthe main wheels divided by the total weight of the plane gives theprojection upon the longitudinal axis of the aircraftof the distance ofthe center of gravity from the center of the main wheels.

Such calculations may be expressed by the formula:

in which CG=distance of center of gravity from main wheels. WNW=weighton nose wheel.

If the nose of the aircraft is utilized as the reference datum:

CG1=distance of new center of gravity from nose of aircraft.

Arm=distance of added weight from nose of aircraft.

If the main Wheels are used as the reference datum:

CG1=distance of new center of gravity from main wheels. Arm=distance ofadded weight from main wheels. Weight in both cases=the weight of theaircraft before the added weight is loaded. Utilizing Formula 3 for eachreference datum:

380.28 inches from nose (47.14= 70,000) (1,000X230) 49.72 inches frommain wheels The center of gravity of an aircraft with respect to anygiven reference datum may also be expressed in terms of percent MACwhich is the ratio of the distance of the center of gravity from theleading edge of the MAC to the width of the MAC multiplied by 100.

The percent MAC may be determined by using the formula:

CG in percent MAC= X 1 00 H=distance from reference datum to center ofgravity. idistance from reference datum to leading edge of and selectingas the center of gravity the rearward limit ofthelvIAC X 100: 15.2 MACUtilizing as the reference datum, the main wheels which are 430 inchesfrom the nose of the a'ircraftfthe permissible limits ofthe MAC will bebetween 30 and 50 inches from the main wheels; the nginus sign allowingfor the fa that the measurements 'of H and Y are in the negafive orforward direction:

Aceording to one present practice, the basic weight of an'aircraft, i.e., without fuel, crew, safety equipment or carge, butincluding allstandard equipment, is determined generally by actually Weighing theaircraft on suitable-scales. The basic center of gravity is thencaleulated By, utilizing suitable formulas such as'Eorrnula's G=. X =1-2% A 1 or 2 above described.

Assuming'that the aircraft is to travel to a predetermined. destinationrequiring a given fuel load, the weight of which'is "reaclilyiascertainable; "a specialist in the Weights and Balances Division'of anairport, taking into consideration the basic weight and basic center ofgravity of the aircraft as well as the weight of the crew, fuel andsafety equipment and the location of such iterris, may 'de termine astandard calculating device, such as a slide rule which is well known tothose skilled in the art, the initial center. of gravityof the aircraft.The payload or' weight of cargo is of course the permissible gross take-9E -Weightrless the basic weighfof the aircraft, fuel, crew and safetyequipment.

Aecoridi'ng to" the present practice, the. cargo. loading r w r, at empt dis ribut t e ea e, in ud passen rs, alongthedength" ofthe"aircraft'sothatthe finalceriter ofi-grav'ity of'the, fully loadedaircraft will fall within the permissible lirnits of its MAC.'-Gene'ral1yf the-'"heaViest'cargois loaded into a compartment which isadjacent to oiibetween the permissible limits of the The weight of thesuccessive items of cargo, "generally indieafed on' eachitem'by "theshipper or manufacturer, andntheirfpjosition in "the aircraft are notedon the manifest as the loading proceeds.

Afte wthe aircraft has been loaded, the manifest is turnd'over to theWeights and Balances Division of the airport, which transfefsthedataon-the manifest to a slide rule which indicates the final or takeoff centei of ravitvotthe aircraft as thus loaded. liblildthefinal'center of gravity thus shown on the slide "rule be outside of thepermissible limits of the MAQ-th'e cargo loading supervisor will'beadvisedltliat the"-cargo is" improperly loaded.- and, must be shifted.Thus, if the planeg-is ta ilsheavy, "cargo must be shifted forward andif the plane" is"noseT-heavy, cargoflnust be shiftedstoward. the rear'ofsthe plan'e. It apparentthat such procedure is time-consuming andcostly butiinustlje followed, for it would be unsafe to attempt to flythe aircraft unless it was i'rbpei'lyllbaded Inasmuch as it is essentialthat the final center of gravity of the loaded aircraft be within thepermissible limits of the MAC for safe take oif, flying and landing pftheair- "craft," the personnersfthe Weights and Balances Divis'idn mustbe highly trained and must perform their work with extreme care, for anyerrors in their calculations might have fatal consequences. As a result,the calculations of the Weights .and Balances Division vmust becarefully checked and re-checked for errors and even with such checking,by reason of the human element involved, there'is no assurance that someerror has not remained undetected.

Inasmuch as the subsequent settings of the slide rule to determine thefinal center of gravity of the loaded aircraft depends upon the accuracy.of the basic center of gravity determination thereof, if any items ofequipment should be added to or removed from the aircraft withoutappropriate entries and calculations being made of the weight added orremoved and the location of such weight, no matter how accurately thesubsequent settings on the slide rule are made for the initial center ofgravity determination'with respect to crew members, fuel and safetyequipment and the final center of gravity determination with respect tocargo, such slide rule determined final ce er b 'g e'v v "may differ matenl y"f the actual finalcenter of gravity of theaircraft.

Even if all'items'aldded to or removed frjdni'the aircraft are properlylisted and calculated, due to'er'rtraneous factors present at the timeof take off, the Slide rule determinedfinal center of gravity "of theaircraft may in fact not beits' actualfinal centenof gravity. Thus, forexample, if the aircraft has been carrying cargo such as coal, thecollection of coal dust in the crevices of the aircraft especially nearthe tail end, may add such a moment that the final center of gravitydetermined by the" slide ule t ug w n e perm ssib e li s f the MA ismisleading because the actual center of gravity may in fact beoutsideofsufch limits. As a result, 'the' aircraft may be tail-heavy,with resultant possibility of crash on take off. In addition,suchfactors as collection ofrnoishire on the" surfaces of the aircraftbefore take off m add a moment that also will cause the actual finalcenter of gravity in time of takeofi to differfrorn the slideride'determinedc'enter of'gravity with resultant possibility of crash oruneconomical fuel consumption duringflight. In addition to" the reasonsabove given for the deviation of theslide rule 'deterrnin'e'd'final'center' 'ofgravity from the aemar'fin'areemerorgravity, if'is verypossible'that the weights of the items of cargo used in thecalculations, if takefi 'from the suhpners markingson'such items, may beinaccurate and such inaccuracy might also cause the actual final centerof gravity of the aircraft to differ from the} slide rfuledterrnihedfinal center ofgravity' with re sultant possible fatal consequences.

Moreover, as fuel is consumed by the aircraft in flight, the center ofgravity of such aircraft may shift and may not be within the limits forsafe landing.

"It'is accordinglyarhourig h I sjof the in entio n to Pr vide a m t and.eqillp h a e'd' y eve an? nskil ed h ffiaticall'y take into account the"actu aircraft and the actual po wi out er or, 4 t the i e, sic' ca o" c.7 triesbn 'e manifest o entry or elimination of items f equi W dr wnespe t v lyt ut n of diistjdirtor moisture, quicklyandaccufatel'yindicate the'actual final'ce'nte'r of gra'j ty of the aircraft, in orderto facilitate checking thatit is within the perr'nissible: limits. setby. the manufacturer for afe ake.

and will r and l i g, all withoutnee tar timee cnsu ns calculations ormanipulati ns of any. se t a d heres' ibility. of humane'rrorsj is,completely el' A Another. objectisto provide, Ipethc a eaui men y whichthe actual Posit on f; cent r Q grav ty m. .e observed at ll' i nes ashe le din Proc eds e as o iss nse with the n ed for. ex en ive hi tinQi'the s in a fully loaded plane which may become necessary to assuresafety when such guidance is not afforded.

Another objectisto' providea method and equipment of the abovety'p'ewhereby, once the actual final center of gravity has been determined,the center o gravity of such aircraft at time of landing maybeautomatically ascertained with butasingle si'1nple"rnanipulatioh basedon the weight reduction dufing fiigh't to" agiv'e'n destination.

saw

cation is negligible.

It is accordingly another object of the invention to provide a methodand equipment of the above type which will permit ready determination ofthe weight data with the aircraft positioned transversely of thedirection of the wind and yet without the need for shifting or adjustingthe weighing equipment or accessories thereof regardless what thedirection of the wind.

According to the invention from its broader aspect, the equipmentcomprises facilities whereby the weight factor is introduced in responseto the weight on the respective wheels to regulate an electric impulserelated thereto. The equipment also comprises facilities to regulate anelectric impulse related to the total moment of such aircraft withrespect to any given reference datum. The electric impulses areconnected in suitable circuits so as to give an indication equal to thetotal moment divided by the total weight or the distance of the centerof gravity from the reference datum.

In a preferred application of the invention, a pair of currentregulating means is actuated by each of the three wheels conventionallyused on aircraft, the current regulating means of each pair beingrelated respectively to the weight on the associated wheel and thedistance of such wheel from any selected reference datum. The threepairs of current regulating means are connected in suitable circuits togive a response corresponding to the sum of the products of the weighton each wheel multiplied by its distance from the selected referencedatum or the total moment of the aircraft with respect thereto.Facilities are provided to set into circuit with such three pairs ofcurrent regulating means, additional current regulating means related tothe sum of the weights on such three wheels. The current regulatingmeans are connected in suitable circuits so as to give an indicationequal to the total moment divided by the total weight or the distance ofthe center of gravity of the aircraft from the selected reference datum.

To this end, in a specific application of the invention, the currentthrough resistance of value proportional to the logarithm of the totalmoment of the aircraft with respect to a given reference datum isopposed by current from a common source through resistance of valueproportional to the logarithm of the total weight of the aircraft. Thequotient of the total moment divided by the total weight is obtainedfrom a variable logarithmic resistance in series with the total weightresistance and said variable resistance is operated preferably by amotor drive controlled by the resultant difference of potential untilsuch difference is eliminated, whereby a suitable scale associated withsaid variable resistance will indicate the quotient of moment divided byweight or the distance of the center of gravity from the referencedatum.

The total moment resistance desirably forms one leg of a Wheatstonebridge and the series connected total weight resistance and variableresistance form another leg, the motor drive being controlled by theoutput of the bridge until the latter is balanced.

In the accompanying drawings in which are shown one or more of variouspossible embodiments of the several features of the invention,

Figs. 1 and 2 are circuit diagrams of one embodiment of the equipment,

Fig. 3 is a circuit diagram of another embodiment thereof,

Fig. 4 is a circuit diagram similar to Fig. 3 with a wind compensatorcircuit added thereto,

Fig. 5 is a front elevational view with parts broken away of a typicalsupporting panel,

Fig. 6 is a longitudinal sectional view taken along line 6-6 of Fig. 5of a typical indicating drum and drive motor,

Fig. 7 is a diagrammatic front elevational view of an indicating scale,

Fig. 8 is a longitudinal sectional view taken along line 8-8 of Fig. 7,and

Fig. 9 is a transverse sectional view taken along line In order tosimplify the description of the circuit and operation of the equipment,it will be assumed that the equipment is designed to measure the centerof gravity of two types of aircraft, type A and type B, eachillustratively having two main wheels and a third wheel which may be anose wheel, it of course being understood that the equipment and circuitcould readily be modified to measure any number of types of aircraft.

In the equipment shown in Figs. 1 and 2 of the drawings, three momentsare utilized to determine the center of gravity, i. e., the moment ofthe weight on each wheel with respect to a reference datum,illustratively the nose of the aircraft.

The equipment utilizes a plurality of substantially iden ticalWheatstone bridge circuits. Each bridge circuit has a pair of balancingresistances 21 and 22 connected at one end to corresponding points 23and 24 with the other ends of said resistances connected tocorresponding negative main 25. A servo-amplifier 26 connected by inputleads 27 and 28 respectively, to points 23 and 24 of each bridge isconnected by lead 29 to a servo-motor 31. The servomotor andservo-amplifier are illustratively of the type put out by the BrownInstrument Division of the Minneapolis- I-Ioneywell Regulator Companyunder the designation Brown Electronik continuous balance unit No.354,574. As shown in Figs. 1, 2, 5 and 6, the servo-motor 31 isoperatively connected by means of a shaft 32 to a rotatable member,desirably a drum 33 which carries wiper means thereon to contactresistances and conducting rings on an associated insulating panel 34 sothat depending upon the position of the drum and the wiper arm, apredetermined amount of resistance may be placed in circuit. Theequipment desirably comprises a plurality of weigh- 1ng scales of anysuitable type, three weighting scales being illustratively provided,designated by the numerals 35, 36 and 37, to measure the weight on thenose wheel and two main wheels respectively.

In the illustrative embodiment herein shown, each scale controls a setof three movable contact arms 38, 39, 41; 42, 43, 44 and 45, 46, 47,respectively which coact with an associated resistance bank 48, 49, 51;52, 53, 54 and 55, 56, 57 respectively to place in circuit that portionof the associated resistance bank related to the value of the weightbeing measured. The movable arm 38 of one of the scales, i. e., scale35, is connected by lead 58 to positive main 59. One end of resistancebank 48 is connected by lead 61 to movable arm 42 of scale 36 and oneend of resistance bank 52 is connected by lead 62 to movable arm 45 ofscale 37. Thus, the resistances 48, 52 and 55 are connected in series.

One end of resistance bank 55 is connected by lead 63 to point 24 ofWheatstone bridge 64. Point 23 of bridge 64 is connected by lead 65 toone end of resistance bank 66, desirably a continuous length of wiremounted on insulating supporting panel 34 associated with bridge 64,said reslstance desirably being arranged as an annulus. Also mounted onpanel 34 concentric with resistance bank 66 and desirably encompassedthereby is a conducting ring 67, a second annular resistance bank 68 anda second conducting ring 69. The conducting rings 67 and 69 are bothdesirably connected to positive main 59 and one end of resistance bank68 is connected by lead 71 to one end of an annular resistance bank 72desirably mounted on an insulating panel 34 associated with Wheatstonebridge 73.

The drum 33 associated with Wheatstone bridge 64 mounts a pair of spacedwiper arms 74 and 75 insulated from each other and designed to contactresistance bank 66 and conducting ring 67; and resistance bank 68 andconducting ring 69, respectively. Thus, depending upon the position ofthe drum 33 and the wiper arms 74 and 75, a predetermined amount ofresistance banks 66 and 68 will be placed in circuit.

Also mounted on panel 34 of bridge 73, concentric with resistance 72 isa conducting ring 76 connected by lead 77 to movable arm 78 ofmultiplier switch 79. Switch 79 has a plurality of fixed contacts 81which may be selectively engaged by said movable arm 78. One of thefixed contacts 81 is connected by lead 82 to common lead183 and each ofthe other fixed contacts 81 has a resistance connected thereto at oneend and designated 84a, 84b, etc. The other end of said resistances 84is connected to common lead 83 which is in turn connected by lead 85 topoint 23 of Wheatstone bridge 73. The drum 33 of said bank 113, 114 and115 and arm 129 of .A and: B, said sections tively with the nose "theaircraft.

bridge? qatfiesafwiper arm .86' whiehis'des'igned to Contact resstance,bankf72and conducting ring 7. so that depending uponthepbs'it'i'on of drum 33 apredetermined amountof resistance bank 72will be placed in circuit.

Point 24 'of'bridge 73 is connected by lead 87 toone end 'of annularres'istance bank88, mounted on panel 34 associated with bridge 89.,,Also mounted on panel 34 concentric with resistance bank '88 is aconducting ring 91, a second annularresistance vbank' 93 and associatedconduct'ingring 92anda thirdannular resistance bank 9 5 and associatedconducting ring 94. The conducting rings 91, 92 and 94 ar e desirablyconnected to positive main 59. One .endp-f annu1ar, resistance bank 93is connected by 'lead 96, to point 24'o-f Wheatstonje bridge 89. Oneen'dof annular resistance bank 95 is connected by lead 97 to point 24ofWhea'ts'tone' bridge9 The drum, 33. associated 'Withbr'idge 89desirably inoun'tsthree longitudinally spaced wiper arms '99, .101 and102. insulated 'ir'omfeach other and designed respectively ;tp}contactannti larresistance bank .95 and conduc'ting ringj94; 'anniil'arresistance bank 93 and conducting ring 92a'nd annular resistance bank 88and conducting ring 91. Thus depending u'pon theposition of drum 33,Ja'predete'rrnmed amount of 'r'esistancebanks 95, 93 and 88 willbeplacedfincircuit.

The'circuit also includes three'Wheats'tone' bridges 103, 104 and105each of which has. an associated panel 34. Each panel 34 mountsrespectively an annular resistance bank 106, 107 and 108 concentric withconducting rings 109, 111 and 112 respectively, a second annularresistance a second conducting ring 116, 117'and 118 respectively. Thedrum 33 associated with each of saidWheatstone bridges 103, 104 and 105mounts a pairof spaced wiper arms 119, 121; 122, 123 and 124,respectively. Each of the wiper arms contacts both a resistance bank anda conducting ring. Arms .119 and 121 contact resistance bank 106 andconducting ring 109; resistance bank 113 and conducting ring 116respectively.

Arm's 122 and 123, contact resistance bank 107 and conductingring 111;resistance bank 114'and conducting ling '117,respectively. Arms. 124 and125 contact resistance bank 108 and conducting ring 112; resistance bank115 and conducting ring 118 respectively. ,Thus, depending upon theposition of the drum associated with said bridges 103 104 'andl'105,"th'ewiper arms carried thereby will place a predetermined amount of theassociated resistanc'e'banks in circuit.

One end of resistance bank 115 of bridge .105 is connected by lead 126to J'the point 23 of bridge 89. The

'end of the associated resistance bank 108 is connected by lead 127topoint 2 4 of said bridge 105.

. The other point 23 'of said bridge 105:is"co nnected by lead 128 tomovable v section C of aircraft selector switch 131. Switch 131desirably has'two other sections, i. e., sections wheel and the two mainwheels of Each of the sections A and B also has a movable arm 132 and133 respectively, said arms being ganged together with'movable 'arrn 129of section C and with the movable arm 7810f multiplier switch 79 so'thatsaid arms will move in nison'upon setting of the knob 134 tothe aircrafttype position.

Each of the sections A, B and C of switch 131 has a plurality of fixedcontacts 135 which may engaged by the associated movable arms 132, 133and 129 respectively. Each section has a plurality of resistances, twoof which are 'illustratively shown and designated .136, and 137,connected respectively. at one end to'v an associated contact 135.

The other ends of said resistances are connected to an associated commonlead 138, 139 and 141 respectively.

Common lead 141 of section C of switch 131 iscon- 'nectedlby lead 142 toone end of resistance 56, the movable arrn 46 of which is connected bylead 143 to positive .m-airit 59. Point,23 of Wheatstone bridge 103 andpoint 24 of Whe'atstone bridge 104 are connected by leads 144 and 145,respectively to movable arms 132 and 133 of sections 8 of saidsectionsAandB are connected by leads I146 147 respectively to one endofresistance 49 and 53, the h k =to positive .frnain :59 as-by leads 148and 149 respectiv ely.

movablearms 39 and .43 of which are connected "The conducting rings 109,111 a A, 'B and C being associated respecbe selectively A and B ofswitch 131, The common leads 138" nd 112 of the bridges -mounted onpanel 34 of bridge 163.

nected by lead 184 to movable arm $103, 104-and IDSare'connectedbylea'ds 151,- 152 and 153 respectively to positive main 59.and:conducting'ring'116 of 'bridge'103 isalso connected to positivemain '59. One

The movable'a'rm 41 of one of the 'sca'lestFig. 2),, i. 'e., scale 35associated with the nose weight, is connected by lead 158 to positivemain 59. One end of resistance'bank 51 is connected by lead 159 tomovable arm 44 of scale .36 and one end of resistance bank 54 isconnected by "lead 161 to movable arm 47 of scale 37. Thus the resistance banks 51, 54 and 57 are connected in series and one end ofresistance -bankl57 is connected by lead 162 topoint 23 of Wheatstonebridge 163.

ioint .24 of bridge 163 is connected by vleadI164T'to movable arm 165 offuel consumption switch 166 said movable am being controlled 'by meansof a knob 167. The switch has a plurality of .fixed contacts 168, one ofwhich is directly connected to common lead169 and the others of whicheach has the end of a resistance 171 affixed thereto respectively, withthe other ends of said resistances being connected to said'common lead169. Although any number of resistances 171 could be provided, dependingupon the number of increments of weight relating to fuel consumption,but two resistances 171a and 17 1b are illustratively identified.

Common lead 169 of switch 166 is connected by lead 172 to one'end ofannular resistance 'bank 173, desirably Also mounted on panel 34concentric with resistance bank 173 is a conducting ring174, a secondannular resistance bank 175 and a second conducting ring 176. Theconducting rings 174- and 176-are'both desirably connected topositive'main 59 and one end of resistance 175 is connected by lead 177to one'end of an'annular resistancebank 178 mounted von a panel34associated withWheatstone bridge 179. The

drum 33 associated with bridge 163 mounts a pair of spaced wiper arms181 and 182 insulated from eachother and contacting resistance bank 173and conducting ring 174; and resistance bank 175 and conducting ring 176respectively. Thus, depending upon the position of drum 33 and wiperarms 181 and 182, a predetermined amount of resistance banks 173 and 175will be placed in circuit.

Also mounted on panel 34 of bridge 179 concentric with resistanceb'ank178 'is a conducting ring 183 con- 185 of multiplier switch 186 which isidentical to multiplier switch'79, correspondingparts having the samereference numerals primedsaid arm 185 being ganged'to move in unisonwith arm 78 of switch 79 upon rotation of knob-134. The

:common lead 83' of switch 186 is connected by lead 187 to point 23 ofWheatstone bridge 179.

The drum 33 of bridge 179 carries a wiper arm 188 contacting resistancebank 178 and conducting ring '183 so that depending upon the position ofthe drum and the Wiper arm 183, a predetermined amount of resistantancebank 178 will be placed in circuit. Point 24 of bridge 179'is connectedby lead 189 to one end of annular resistance bank 191 mounted on panel34 of bridge 98. Also mounted .on panel 34- concentric with resistance191 is a conducting ring 192, a second annular resistance bank 193 and asecond conducting ring 194.

The conducting rings 192 and 194 are both connected to positive main 59.One end of resistance bank 193 is connected by lead 195 to movable arm196 of a second aircraft selector switch 197, said arm 196 being gangedto move in unison with the arms of selector switch 131 upon setting ofthe latter by control knob 134.

Switch 197 has a plurality of fixed contacts 198 which may successivelybe engaged by movable arm 196.. The contacts 198 are connectedrespectively by a plurality of leads 199 to the movable arms 201 of afuel moment "switch 202. This switch has a plurality of sectionscorresponding .to the number of types of aircraft-to bemeasured "bythee'q'uipinenfltwo sections A andB being illustratively shown, each havinga movable arm 201 ganged .datum other pending upon the 245, 246 and 247to measure to move in unison with the movable arm 165 of fuelconsumption switch 166.

Each of the sections of switch 202 has a plurality of fixed contacts 203which may selectively be engaged by the associated movable arms 201. Oneof the fixed contacts is directly connected to an associated common lead204 and each of the other fixed contacts has a resistance connectedthereto at one end, two resistances 205a, 205b, being illustrativelydesignated. The free end of the resistances 205 of each section isconnected to an associated common lead 204, said leads being connectedtogether by lead 206, the leads 204 being connected by lead 207 to point23 of bridge 98.

The drum 33 of bridge 98 carries a pair of wiper arms 208, 209 insulatedfrom each other and designed to con- ,tact resistance bank 193 andconducting ring 194; and

resistance bank 191 and conducting ring 192 respectively so thatdepending upon the position of drum 33 and wiper arms 208, 209 carriedthereby, a predetermined amount of resistance banks 193 and 191 will beplaced in circuit.

In the circuit shown in Figs. 1 and 2, the nose of the aircraft isselected as'the reference datum. The center of gravity may also bedetermined by selecting a reference than the nose of the aircraft. Thus,in the embodiment shown in Fig. 3, the main wheels are selected as thereference datum and in such case only the moment of the nose wheel needbe taken into account to determine the center of gravity.

The equipment shown in Fig. 3 also utilizes a plurality of substantiallyidentical Wheatstone bridge circuits. Each bridge has a pair ofbalancing resistances 231, 232

connected at one end to points 233 and 234 of the associated bridge withthe other ends of said resistances being connected to negative main 235.

A servo-amplifier 236 connected by input leads 237 and 238 respectively,to points 233 and 234 of each bridge is connected by lead 239 to aservo-motor 241. Motor 241 is operatively connected by means of a shaft242 to a rotatable member desirably a drum 243 which carries wiper armsto engage associated resistances and conducting rings mounted on anassociated upright panel 244 so that deposition of the drum and thewiper arms, a predetermined amount of resistance may be placed incircuit.

The equipment desirably comprises a plurality of weighing scales of anysuitable type, three weighing scales being illustratively shown,designated by the numerals the weight on the nose wheel and two mainwheels respectively.

In the illustrative embodiment herein shown, scale 245 associated withthe nose wheel, controls a set of three movable contact arms 248, 249and 251 and the scales 246 and 247 associated with the main wheels eachcontrols a single movable arm 252 and 253 respectively.

The movable contact arms 248, 249 and 251 coact with associatedresistance banks-254, 255 and 256 respectively, and movable contact arms252 and 253 coact with resistance banks 257 and 258, said movable armsplacing in circuit that portion of the associated resistance bankrelated to the value of the weight being measured. The movable arm 248of one of the scales, i. e., the scale 245, is connected by lead 259 topositive main 261. One end of resistance bank 254 is connected by lead262 to movable arm 252 of scale 246 and one end of resistance bank 257is connected by lead 263 to movable arm 253 of scale 247. Thus, theresistance banks 254, 257 and 258 are connected in series.

One end of resistance bank 258 is connected by lead 264 to point 233 ofWheatstone bridge 265. Point 234 of bridge 265 is connected by lead 266to one end of an annular resistance bank 267 desirably a continuouslength of wire mounted on supporting panel 244. Also mounted on panel244 concentric with resistance bank 267 is a conducting ring 268, asecond annular resistance bank 269 and associated conducting ring 271and a third annular resistance bank 272 and associated conducting ring273. The conducting rings 268, 271 and 273 are desirably connected topositive main 261. One end of resistance bank 269 is connected by lead274 to one end of an annular resistance bank 275 desirably mounted oninsulating panel 244 associated with Wheatstone bridge 276 and one endof resistance bank 272 is connected by lead 277 to point 233 ofWheatstone bridge 278.

The ,drum 243 associated with bridge 265 carries a plurality oflongitudinally spaced wiper arms 279, 281 and 282 insulated from eachother and designed to contact resistance bank 272 and conducting ring273; resistance bank 269 and conducting ring 271 and resistance bank 267and conducting ring 268, respectively. Thus, depending upon the positionof drum 243 and the wiper arms 279, 281 and 282, a predetermined amountof the associated resistance banks will be placed in circuit.

Also mounted on panel 244 of bridge 276 concentric with annularresistance 275 is a conducting ring 283 connected by lead 284 to point233 of bridge 276. Point 234 of bridge 276 is connected by lead 285 tocommon lead 286 of aircraft selector switch 287. The switch 287 has aplurality of fixed contacts 288 which may be selectively engaged by amovable contact arm 289 controlled by a suitable knob 291. Each fixedcontact has a resistance 292 connected at one end thereto respectively,the other ends of said resistances being connected to common lead 286.In the illustrative embodiment herein, two resistances 292 aredesignated 292a, 292b.

Movable arm 289 is connected by lead 293 to one end of resistance 255,the movable scale arm 249 engaging said resistance being connected topositive main 261.

The drum 243 associated with bridge 276 desirably carries a wiper arm294 designed to contact resistance bank 275 and conducting ring 283 sothat depending upon the position of drum 243 and wiper arm 294, apredetermined amount of resistance bank 275 will be placed in circuit.Point 234 of bridge 278 is connected by lead 295 to common lead 296 offuel consumption switch 297. Switch 297 has a plurality of fixedcontacts 298 which may selectively be engaged by movable arm 299. One ofthe fixed contacts 298 is directly connected to common lead 296 and eachof the other fixed contacts 298 has one 5 end of an associatedresistance 301a, 301b, etc. connected thereto respectively, the otherends of said resistances being connected to common lead 296.

Movable arm 299 is connected by lead 302 to one end of annularresistance bank 303 mounted on panel 244 of bridge 278. Also mounted onpanel 244 concentric with resistance bank 303 is a conducting ring 304,a second annular resistance bank 305 and a second conducting ring 306.The conducting rings 304 and 306 are both desirably connected topositive main 261 and one end of resistance bank 305 is connected bylead 307 to one end of annular resistance bank 308 mounted on panel 244associated with bridge 309. Drum 243 of bridge 278 desirably mounts apair of wiper arms 311 and 312 insulated from each other and designed tocontact resistance bank 303 and conducting ring 304; and resistance bank305 and conducting ring 306 respectively so that depending upon theposition of said drum and the wiper arms 311, 312, a predeterminedamount of the associated resistance banks will be placed in circuit.

Also mounted on panel 244 of bridge 309 concentric with resistance bank308 is a conducting ring 313 connected by lead 314 to point 233 ofbridge 309. Point 234 of bridge 309 is connected by lead 315 to one endof annular resistance bank 316 mounted on panel 244 of bridge 317.

Drum 243 of bridge 309 carries a wiper arm 318 engaging resistance 308and conducting ring 313 so that depending upon the position of the drumand the wiper arm, a predetermined amount of resistance 308 will beplaced in circuit.

Point 234 of bridge 317 is connected by lead 319 to movable arm 321 of aselector switch 322, said movable arm 321 being ganged with movable arm289 of switch 287 and controlled by knob 291. Arm 321 is designedsuccessively to engage a plurality of fixed contacts 323 connectedrespectively to the leads 324 to the movable arms 325 of fuelconsumption moment switch 326, said arms 325 being ganged with themovable arm 299 of fuel consumption switch 297 so that said arms willmove in unison upon rotation of knob 327.

The switch 326 desirably comprises a plurality of sections dependingupon the number of types of aircraft to be measured by the equipment. Inthe illustrative embodiment, the switch has two sections A and B. Eachsection has a plurality of fixed-contacts 328 selectively engaged by theassociated movable contact arm 325. One of the contacts 328 of eachsection is connected directly to an associated common lead 329. Theother fixed contacts of section A of switch 326 are connectedrespectively to one end of a plurality of resistances 331a,

331b, etc, the other end of said resistances being connected to theassociated common lead 329. The common leads 329 are connected "by "lead332 and common lead 329 is connected by lead 333 to one end of annularresistance bank 334 also mounted on panel 244 of bridge 317. The annularresistance banks 316 and 334 each has an associated conducting ring 335and 336 mounted on said panel 244, said conducting rings being connectedto positive main 261.

, Drum 243 of bridge 317 mounts a pair of wiper arms 337 and 338insulated from each other and designed to engage resistance bank 334 andconducting ring 336; and resistance bank 316 andconducting ring 335respectively, so that depending upon the position of the drum and thewiper arms, apredetermined amount of the associated resistance will beplaced in circuit.

The point 233 of bridge 317 is connected by lead 339 to annularresistance bank 341 mounted on panel 244 of bridge 342. Also mounted onsaid panel 244 concentric with resistance bank 241 is a conducting ring343, 'a second annular resistance bank 344 and a second conducting ring345. The conducting rings 343 and 345 are both connected to positivemain 261. One end of annular resistance bank 344 is connected by lead346 to point 234 of bridge 342.

Point 233 of bridge 342 is connected by lead 347 to movable arm 348 ofaircraft selector switch 349. Movable arm 348 is ganged with movable arm289 of switch .287 and with movable arm 321 of switch 322 so that saidarms will move in unison. Switch 349 is identical to switch 287 andcorresponding parts have the same reference numerals primed. Common lead286' is connected by lead 351 to one end of resistance 256, the movablescale arm 251 engaging said resistance being connected to positive main261.

Drum 243 of bridge 342 carries a pair of wiper arms 352 and 353insulated from each other and designed to engage resistance bank 344 andconducting ring 345; and resistance bank 341 and conducting ring 343respectively, so that depending upon the position of the drum 243 andWiper arms 352 and 253, a predetermined amount of resistance 344 and 341will be placed in circuit.

In the circuits shown in Figs. 1 and 2 and in Fig. 3, but three weighingscales are provided. In the circuit shown in Fig. 4, four weighingscales 361, 362, 363 and 364 are provided which are so spaced that anyone of the scales may carry the nose wheel of the aircraft to bemeasured and two of the remaining three scales will carry the two mainWheels. Thus, the aircraft may be so positioned on the scales that it isat substantially right angles to the direction of the wind, to minimizethe efiect thereof on the weight of the aircraft as indicated by thescales.

The circuit shown in Fig. 4 utilizes a pair of substantially identicalWheatstone bridge circuits. Each bridge has a pair of balancingresistances 362 and 363 connected at one end to points 364 and 365 ofthe associated bridge with the other ends of said resistances beingconnected to negative main 366.

A servo-amplifier 367, connected by input leads 368 and 369 respectivelyto points 364 and 365 of each bridge, is connected by lead 371 to aservomotor 372. Motor 372 is operatively connected by means of a shaft373 to a rotatable member, desirably a drum 374 which carries wiper armsto engage associated resistances and conducting rings mounted on anassociated panel 375 so that depending upon the position of the drum andthe wiper arms, a predetermined amount of resistance may be placed incircuit.

In the illustrative embodiment, the scales 361, 362, 363 and 364 eachcontrols apair of movable contact arms 376, 377; 378, 379; 381, 382 and383, 384, respectively. The contact arms 376, 378, 381 and 383 coactwith associated resistance banks 385, 386, 387 and 388 respectively andthe contact arms 377, 379, 382 and 384 coact with associated resistancebanks 389, 391, 392 and 393 respectively, said movable arms placing incircuit that portion of the associated resistance bank related to thevalue of weight being measured.

Gne end of resistance bank 389 is connected to positive main 394. Themovable arm 377 of scale 361 is connected by lead 395 to one end ofresistance bank 391.

The movable arm 379 of scale 362 is connected by lead 396 to one end ofresistance bank 392. The movable arm 382 of scale 363 is connected bylead 397 to one end 12 of resistance bank 393. Thus, the resistancebanks 389, 391, 392 and 393 are connected in series.

The movable arm 384 of scale 364 is connected by lead 398 to point 364of Wheatstone bridge 399. Point 365 of bridge 399 is connected by lead401 to one end of annular resistance bank 402 mounted on panel 375 ofbridge 399. Also mounted on panel 375 concentric with resistance bank402 is a conducting ring 403, a second annular resistance bank 404 and asecond conducting ring 405. The conducting rings 403 and 405 are bothdesirably connected to positive main 394. One end of annular resistancebank 404 is connected by lead 406 to one end of annular resistance bank407, desirably zrggunted on insulating panel 375 associated with bridgeThe drum 374 associated with bridge 399 carries a pair of Wiper arms 409and 411 insulated from each other and designed to contact resistancebank 402 and conducting ring 403; and resistance bank 404, andconducting ring 405, respectively. Thus, depending upon the position ofdrum 374 and wiper arms 409 and 411, a predetermined amount of theassociated resistances will be placed in circuit.

. Also mounted on panel 375 of bridge 408 concentric with resistancebank 407 is a conducting ring 412 connected by lead 413 to point 365 ofbridge 408. The drum 374- associated with bridge 408 carries a wiper arm414 designed to contact resistance bank 407 and conducting ring 412.Thus, depending upon the position of drum 374 and wiper arm 414 apredetermined amount of resistance 407 will be placed in circuit.

()ne end of each of the resistance banks 385, 386, 387 and 388 isconnected to positive main 394. The movable arms 376, 378, 381 and 383associated with said resistance banks respectively, are connected tofixed contacts 415, 416, 417 and 418 of relays 419, 421, 422 and 423respectively. The movable arms 424, 425, 426 and 427 of said relays areconnected together by lead 428, which in turn is connected to movablearm 429 of aircraft selector switch 431.

Arm 429 selectively engages a plurality of fixed contacts 432 connectedrespectively to one end of a plurality of resistances 433, 434, etc.,the other end of said resistances being connected to common lead 435which is connected by lead 436 to point 364 of bridge 408.

The scales 361, 362, 363 and 364 each controls a normally openmicro-switch 437, 438, 439 and 441 respectively, the movable contactarms 442, 443, 444 and 445 of which are connected to positive main 394.The fixed contacts 446, 447, 448 and 449 of said micro-switches areconnected respectively by leads 451, 452 and 453 and 454 to one side ofthe coils 455, 456, 457 and 458 of relays 459, 461, 462 and 463, theother side of said coils being connected to negative main 366.

The relay 459 has .a fixed contact 464 and a movable contact arm 465normally spaced therefrom; the relay 461 has a pair of fixed contacts466, 467 each having a movable contact arm 468, 469 normally spaced fromthe associated fixed contact and ganged to move in unison; the relay 462has three fixed contacts 471, 472, 473, each having a movable contactarm 474, 475, 476 normally spaced therefrom and ganged to move in unisonand the relay 463 also has three fixed contacts 477, 478 and 479 eachhaving a movable contact arm 481, 482, 483, normally spaced therefromand ganged to move in unison.

Fixed contact 464 of relay 459 is connected to positive main 394.Movable arm 465 is connected by lead 484 to fixed contact 466 of relay461 and by leads 484, 485 to fixed contact 472 of relay 462. Movable arm468 of relay 461 is connected by leads 486 and 487 to fixed contacts 477and 471 of relays 463 and 462 respectively. Fixed contact 467 of relay461 is connected to positive main 394 and movable arm 469 is connectedby lead 488 to fixed contact 473 of relay 462.

Movable arm 474 of relay 462 is connected by lead 489 to one side ofcoil 491 of relay 421. Movable arms 475 and 476 of relay 462 areconnected by leads 492 and 493 to fixed contacts 478 and 479 of relay463. Movable arms 481, 482 and 483 of relay 463 are connected by leads494, 495 and 496 respectively to one side of coils 497, 498 and 499 ofrelays 419, 422 and 423 and the other side of coils 497, 491, 498' and499 are connected to negative main 366 to complete the circuit.

23,940 13 0 r Calculation of resistances (b) DI the successiveresistances 292a, '292b of switches In determining the value of theresistances utilized and 349 shown in and 0f the successive th ,7resistances 433, 434 of switch 431 shown in Fig. 4, m e ell-cults abovedescnb the followmg limits for said resistances being assoclated withthe distance the e ui ment will be assumed.

q P 5 along the longltudlnal ax1s from the mam wheels to I the nosewheel; the logarithm of each distance is determined and mul- Welght onScalem Pounds Minimum Maximum i li d b 1 0()() For the circuit shown inFigs. 1 and 2, the following Nose Wheel 4,000 20,000 tabulation may bemade: Left Main Wheel 15, 000 70, 000 Right Main wheel 15, 000 70, 000

Distance in Inches From 0 i i H V Nose of Aircraft t Min. Log. Res. Max.Log. Res.

Distance in Inches 0.1011 1011 tudinalAxis 100 2000 000 100 2- 2,2 {mmof i Mlnimum Malflmum' 430 2.032 2, 033 010 2. 705 1 2,785 430 2. 033 2,033 010 2. 785 2, 785

Nose Wheel 100 100 Mam Wheels 430 010 Thus, the values of reslstances136 and 137 of sectron A of switch 131 for two types of aircraft withthe minimum and maximum limits above set forth are 2,000 2 g gg g "j Z33 3% and 2,204 ohms respectively, the values of resistances 136 Fi. sand resistance banks 305, ass, 387 and ass of and 1 i B and C are 2633and Fig. 4, the logarithm of the weight to be applied to the 23; gfishown in Figs 3 and 4 the scales associated with such resistance banksis determined lowing tabulation may be made.

and such logarithm is multiplied by 1,000 for ease in calculation. VI

For the circuits shown in Figs. 1 and 2 and in Fig. 3, the followingtabulation can be made: Min. Log. Res. Max. Log. Res.

III

Distance in Inches from Main Wheel to Nose s P0111108 Mm Mm Log, Wheel330 2.510 2, 510 450 2. 053 2,055 Thus the values of resistances 292aand 433 is 2 519 N Whel 4, 000 a. 002 3, 002 20 000 4.301 4,301 Leiimeln wheel 15, 000 4.170 4,170 701000 4.845 4,0 ohms and the value ofresistance 292b and 343 15 2,653 Right Main Wheel 15,000 4,170 4,170 70,000 4.245 4,045 40 h s,

With the nose of the aircraft as the reference datum,

as is used in the circuit shown in Figs. 1 and 2, the moments about thenose due to the weight on the nose wheel and each of the two main wheelsmay be determined by multiplying the weight on the wheel by its distancefrom the nose of the aircraft and the total Thus, the value ofresistance banks 49, 255 and 256 will be from 3,602 ohms to 4,031 ohmsand the value of rehsistance banks 53 and 56 will be from 4,176 to 4,8450 ms.

i the clrculttfihown as y f moment may be found by adding the individualmoments. Sc can carry 6 Dose W or mam w e The logarithm of theindividual moments may be reslstance banks 385, 386, 387 and 388 mustcover the found by adding the logarithms of the weight on the rangebetwgen the mmlmu-m Welght of 4000 Pounds and wheel and the logarithm ofthe distance of such wheel the maximum weight of 70,000 pounds and thevalue of from the nose of the aircraft and such 10 l garlthm ls gafisofsuch resistance banks 1s from 3,602 ohms to 4,845 multiplied by LOOQfollowing tabulation may be Each 100 pounds of weight to be applied tothe scale made: VII l associated with each resistance is made tocorrespond to one ohm of res1stan ce 1n ascertalnmg the value of theLogarithm of resistance banks 40, 52, 55 and 51, 54, 57 of Figs. 1Momentag Minimum a um and 2; resistance banks12S4,2 2573, 25; of Fig. 3and resistance banks 389, 39 39 39 of ig. 4. 1 For the circuits shown inFigs. 1 and 2 and in Fig. 3, Nose Wheel (BJZOZH'OWXLOOO 1:38 Hgwxmoo thefollowing tabulation can be made: 60 Left Main ,6 )X1,000= (-845+2,785)1,000== 1V RlghtMainWheel-.. (4.170+2,033) 1,000= (4.s45+2,7s5) 1,000=

' h Min. R Ma R Welg tmPounds on x es 5 Thus the value of reslstancebanks 106, 107 and 108 of bridges 103, 104 and 105 respectively,associated g giflg g t $1888 381% with the nose wheel moment and each ofthe two main Right Main wheel 15,000 150 70,000 700 wheel moments isfrom 5,602 to 6,505 ohms and from 6,809 dto 7,630 ohms respectig elld0 0h/ d In etermining moments, i 0 inc poun s is b g lg 3 66 fi ai banlks51.and i made to correspond to one ohm, the value of resistance 6 mm to0 ms, an CW 116 0 reslstance an 5 banks 113, 114 and 115 of bndges 103,104 and 105 of 52, 55, 54, 57, 257, 258 will be from 150 to 700 ohms.Fig 1 may be determined as follows;

For the circuit shown in Fig. 4 as any one of the scales can carry thenose wheel or a main wheel, the resistance VIII banks 389, 391, 392 and393 must cover the range between 5 1 l the minimum weight of 4,000pounds and the maximum Moment Mlmmum Maxlmum weight of 70,000 pounds andthe value of each of such resistance banks is from 40 to 700 ohms. N 5Wk 1 100 4,000 160 20,000 To determine the values: 8 Ge 10,000 10, 000(a) 0f the successive resistances 136, 137, etc. of sec- LeftMalnWheelWfiss %26 =4,270

tions A, B and C of switch 131, shown in Figs. 1 and 2, associatedrespectively with the distance along Right m wheel i w= W 270 thelongitudinal axis from the nose of the aircraft mom to the nose wheeland to each of the main wheels;

Thus, thevalue. of; resistance, hank,113 is. from 40 to320, ohms-and thevaluesof each resistance bank 114 and. 1'15 is.f1iom 645 to 4,270 ohms.

As the. resistance banks 334 of bridge 317 and resistance bank 341 ofbridge 342 of Fig. 3, respond respectively to the take oif' moment andlanding moment and as the minimum moment of the circuit shown in Fig. 3is equal to 330 times 4,000 or 1,320,000'and the maximum moment, 450times 20,000 or 9,000,000 and since 10,000 inch pounds corresponds toone ohm, the vglue of resistance banks 334 and 341 is-from 1'32 to.9.00ms.

To; find the sum of the individual moments due to the. weight on thenose wheel and each of thetwo main wheels, the, individual moments areadded' by connecting the resistances 1-13, 1-14- and 115 inseries inFig. 1; and 2. The resistance, bank 93 of bridge 89 covers the rangefrom the minimum to the maximum sum of the moments divided by 10,000.-Thus the minimum moment is equal to 1,330 ohms and the maximum mo-'[11611118 equal to 8,860 ohms and the, value of resistance bank: 93 onbridge 89- is' from, 1,330 to 8,860 ohms.

The. resistance banks; 88; and 95 of bridge 89, and resistanceabank193.of: bridge, 9B of: Figs. 1 andv 2' extend from the logarithm multipliedby 11,000 of, the minimum total moment to that of the maximum totalmoment. The following tabulation maybe, made:

Minimum moment 400,000 6,450,000 6,450,000 13',300,000 1,000. log.1.3,300,0.00.=7,.12,4

Maximum moment: 3,200,000-I- 42,700,000-l- 42,700,000 =88, 600,000-1,000 log.8'8,6100,000=7,947

Thus, the value of resistance banks 344 or 316,extends is from 7,124 to7,947 ohms.

The resistance banks 344 and 316 of bridges 342 and 317 of Fig. 3 extendfrom the logarithm times. 1,000 of the minimum total moment to thattimes 1,000. of the maidri'mum moment. The following tabulation may bema e:

Minimum moment=330 4,000: 1,320,000 1,000 log.1,320,000=6,121

Maximum moment=450 X 20,000: 9,000,000

Thus, the value of resistance banks 88, 95 and. 193 from 6,121 to 6,954ohms.

To determine the sum of the weights on the nose wheel and the two mainwheels, the resistances associated with such weights are connected inseries. The value of resistance bank 66 of bridge 64 and resistance bank173 of bridge 163 of Figs. 1 and 2, of resistance bank 267 and 272 of.bridge 2,65 and resistance bank 303 of bridge 278 of Fig. 3 and ofresistance blank 402. of bridge 399 of Fig; 4' extends from the minimumto the maximlm sum of such weights. If each 100 pounds of weight to beapplied to the scale associated with each resistance. is made tocorrespond. to. one ohm of resistance, we find:

The value of resistance bank 68 of bridge 64, and resistance bank 175 ofbridge 163 of Figs. 1 and 2; of resistance bank 269 of bridge 265 andresistance bank .305 of bridge 278 of Fig. 3 and of resistance bank 404of bridge 399 of Fig. 4 is determined by ascertaining the 15 logarithmof the minimum total weight and maximum total weights and multiplyingsuch logarithm by 1,000.

Thus, thevalues ofresistance banks 68, 175, 269, 305 and 404 is from4,531- to 5,204 ohms.

The resistances 1 71a, 1711) of fuel consumption switch 166 of Figs. 1and 2, and resistances 301a and 301b of fuel consumption switch 297 ofFig. 3 are related to predetermined amounts of fuel consumed. Thus, for.example, resistances 171a and 301a are related to 500 gallons' or 3,000pounds and resistances 1 711 and 3111b to 1,000-gallons or 6,000.pounds. To determine the values of such resistances, the weight of fuelis divided by 100. Thus, the following tabulation can be made;

XII-I- Weight. Resistance Fuel Consumed pounds Ohms 500 gallons, 3, 00030 ,000 sa1 Qns-----.-,-- 0 60 turns a AIRCRAFT Fuel consumed Weigh-tMoment Resistance TYPE B AIRCRAFT The values of resistance 205a ofsection A of switch 202 is 120.6 ohms; resistance 205b of section A hasa value of 241.2 ohms. ResistanceZllSa of section B has a value of 180ohms and resistance 2135b of section B has avalue of 360 ohms.

Assuming that the main wheels of the aircraft have been selected as thereference datum and the average distance of such fuel is 402 inches fromthe. nose or 28 inches from the main wheels for a type A aircraft and600 inches from the nose or 10 inches from the main Lvheelsdfor a type Baircraft, the following'tabulation can e ma e:

The value o r sistanc 331a o ecti n A f Switch 326. is 3.4 ohms,resistance 3311) or" section A has a value of 16.8. ohms. Resistance331a of section B has a value 17 of 3 ohms and resistance 3151b ofsection B has a value of 6 ohms.

To determine the distance of the center of gravity of the aircraft, froma given reference datum, the total moment is divided by the totalWeight. This may be expressed by the formula:

Log.CG=-log.total moment1og.total weight or Log.total moment=log.totalweight-l-logCG The resistance banks 72 and 128 of the two bridges 73 and179 related to center of gravity extend from the logarithm multiplied by1,000 of a value somewhat below the minimum distance of the center ofgravity from the reference datum to a value somewhat in excess of themaximum distance.

As such minimum and maximum distances of the center of gravity for thetype A aircraft are 380 and 400 inches, the resistance values ofresistance banks 72 and 128 are set to a range of from 360 to 420inches. The following tabulation can be made:

XVI

Log.

Thus, the values of resistance bank 72 of bridge 73 and resistance bank178 of bridge 179 are from 2,556 to 2,623 ohms.

In order that the resistance banks 72 and 178 of value from 2,556 to2,623 ohms may be used to indicate the center of gravity for the largertype B aircraft, the following calculations are made:

The center of the scale for the center of gravity of the type A aircraftis midway between 360 and 420, i. e., 390 inches. Let it be assumed thatthe center of the scale for the type B aircraft is 565 inches.

The logarithm of the ratio of the two centers of the scales is 565 logwhich, when multiplied by 1,000 equals 161 ohms. This value is themultiplying factor for utilizing the resistance banks 72 and 178 of2,556 to 2,623 ohms for the type B aircraft. Thus, the value ofresistances 84a and 84a of multiplying switches 79 and 186 are 161 ohms.

As mid-point on the scale for the center of gravity of a type A aircraftis 390, the logarithm of this amount multiplied by 1,000 is equivalentto 2,591 ohms. Similarly, the mid-point on the scale for the center ofgravity of a type B aircraft is 565, the logarithm of which multipliedby 1,000 is equivalent to 2,752 ohms.

As the multiplying factor to convert the center of gravity scale from atype A aircraft to a type B aircraft is 161 ohms, this amount added tothe ohmic value of the logarithm of the selected limits of 360 and 420inches or 2,556 and 2,623 ohms respectively will give limits of 2,717and 2,784 ohms.

The anti-logarithms of such resistances divided by 1,000 is 521 and 608inches respectively. Thus, the limits of the scale for a type B aircraftis from 521 to 608 inches, which extends beyond the minimum and maximumlimits of the type B aircraft, i. e., from 545 to 585 inches.

Thus one and the same center of gravity resistance bank can be utilizedfor any of a wide variety of aircraft types by introducing theappropriate multiplying factor according to the principle above setforth.

The drums 33 of bridges 73 and 179 through suitable mechanical orelectrical means may rotate a pointer P shown in Fig. 7 which has avertically adjustable rectangular panel 501 to the rear thereof. Thepanel 501 desirably has a plurality of distinct scales 502 one for eachof the types of aircraft for which the system is adapted and the panel501 is so controlled by the control knob 134 as by a gear and rackarrangement 503 as to cause the correct scale to enter into registrywith the pointer P upon turning the knob to the selected type aircraft.

The indications on the scale markings may be spread over only degrees ofare forexample, to facilitate ease in reading regardless of the numberof types of aircraft to be measured by the equipment.

While it is preferred to utilize a plurality of distinct scales toindicate the center of gravity position for various types of aircraft,by introducing an appropriate multiplier factor for each type largerthan the smallest as above set forth, it is of course understood that asingle scale could be employed to cover the entire range for variousair- ;raft small and large with the omission of the multiplying actor. vI

As the distance of the center of gravity, from the reference datum foundby the circuits shown in Figs. 3 and 4 is with respect to the mainwheels, the range of resistance banks 275, 308 and 407 may be equal to1,000 times the logarithms of the distances of the centers of gravitytherefrom between limits which extend beyond the minimum and maximum tobe measured, to give the range of resistance values for resistance banks275, 30,8 and 407.

As previously described, the type B aircraft has its range of center ofgravity at most 608 inches and at least 521 inches from the nose, thedistances of such centers of gravity from the main wheels being from 2to 89 inches. The type A aircraft has its range of center of gravity atmost 420 inches and at least 360 inches from the nose, the distance ofsuch center of gravity from the main wheels being from 10 to 70 inches.

As the limits of center of gravity are from 2 inches to 89 inches, thefollowing tabulation can be made:

XVII

1000 logarithm 2:301 1000 logarithm 89:1,949

Thus, the value of each resistance bank 275, 308 and 407 is from 301 to1,949 ohms and the drums associated with said resistance banks arecalibrated from 2 to 8 inches.

The indicating scale calibrated in inches for type A aircraft from 360to 420 may be translated to percentage MAC as previously indicated sothat both the center of gravity and percent MAC will be indicated. Q

For the type B aircraft if the indicating scale center of gravity rangeis from 521 to 608 inches and the leadmg edge of the MAC is 521 inchesfrom the nose and has a width of 197 inches, the limiting values of MACare:

Thus, the MAC indicating scale for the type B aircraft may be calibratedin percentages from 0 to 44.2 corresponding to a range of center ofgravities of from 521 to 608 inches.

OPERATION The basic principle of operation of the equipment will beclear from the following brief description of the circuit shown in Fig.3.

The weight of the aircraft on the scales 245, 246 and 247 will placethat portion of the series connected resistance banks 254, 257, and 258in circuit of ohmic value equal to the total weight divided by 100. Theweight resistance banks 254, 257 and 258 form one leg of bridge 265 andthe resistance bank 267 forms another leg of said bridge which, when thebridge is balanced, is set to a resistance value corresponding to thatof the series connected resistance banks and at the same time theassociated resistance 269 is set to a value proportional to thelogarithm of the weight and is in series with resistance bank 275 ofbridge 276 to form one leg of said bridge.

The resistance bank 255 controlled by nose wheel scale 245 and theresistance 292a of switch 287 in series therewith are of ohmic valuesrespectively proportional to the logarithm times 1,000 of the weight onthe nose wheel scale and the distance of the nose wheel from the mainwheel. The combined value of resistance bank 255 and resistance 292a isproportional to the logarithm times 1,000 of the moment of the nosewheel with respect to the the type A position. (Fig. 7) associated withthe type A aircraft will be moved main wheels and such series connectedresistances form another leg of bridge 276.

As the bridge 276 will normally be unbalanced, the motor 241 will rotatedrum 243 until a portion of resistance bank 275 will be placed incircuit that is equal in value to the diiference between the combinedvalues of. resistance bank 255 and resistance 292a; and the value ofresistance bank 269.

'An indication correlated with resistance bank 275 which is theanti-logarithm of a multiple of the difference of resistance designatesthe position of the center of gravity of the aircraft as the quotient.

Specifically to illustrate the operation of the equipment abovedescribed, it will be applied to a type A aircraft of the followingpertinent specifications:

is 355 inches from the nose.

Referring to Figs. 1 and. 2, the aircraft is positioned $011131 its nosewheel rests upon scale 35 and its two main wheels rest on scales 36 and37 respectively. The knob 134- is turned to set the aircraft selectorswitch 131 to As a result the scale on panel 501 intothe range ofpointer P. The movable arms 132, 133 and 129 of sections A, B and C ofsaid switch engage the fixed contacts 135 associated with the respectiveresistances 136 and the movable arms 78 and 185 of multiplier switches79 and 186 engage the associated fixed contacts '81 and 81'respectively. In addition, the movable arm of switch 197 engages theassociated fixed contact Each movable arm 39, 43 and 46 of the weighingscales will tap off that portion of the associated resistance banks49,53 and 56 of ohmic value equal to the logarithm of the weightmultiplied by 1,000 as illustrated in tabula- ,tion II- I. Accordingly,assuming that the weight on scale 35 is 10,000 pounds and the weights oneach of the scales 36 and 37 is 30,000 pounds, the values of resistance;banks;49, 53 and .56 in circuit will be 4,000, 4,477 and .4,'477-ohrnsrespectively. Simultaneously, the movable arms-38, 42, .45 and 41, 44,and 4'7 ofv the scales will tap off that portion of the resistance banks48, 52; and 55 and the resistances 51, 54, 57 of ohmic value equal tothe weight .divided by one hundredas illustrated by tabulation IV. Thus,the value of resistances 48 and 51; 52 and 54; 55 and 57; will be 100,300 and 300 ohms respectively.

The resistances 136 of sections A, B and C of selector switch 131 placedin circuit by the rotation of the movvable arms 132, 1 33 and 129thereof for the. type A position; are associated respectively with thedistance frotnpthe. nose of the, aircraft .to the. nose wheel and toeach of the main wheels. Such distances for the type A aircraft are asabove noted, 100 inches to the nose wheel and 430inches to each of themain wheels. The value ofresist-ances136, of sections A, B and C areequal .to the. logarithm. of the. related distancev multiplied by 1,000as illustrated in tabulation V. Thus, the value .of. resistances 136 ofsections A, Band C are 2,000, 2,633 and 2,633 ohms respectively.

The resistance bank 49 and. resistance 136 of section A of switch 131which are connected in series from .positive main 59 to point 23 formone leg of bridge 103 and the annular resistance bank 106 on panel 34'forms another leg of said bridge 1 03. As resistance ,gagesthat portionof resistance 106 to place 6,000 ohms in. circuit, when servo-motor 31is de-energized and drum ,33jstops. rotating. Thus, there is placed. incircuit a resistance which is proportional to the logarithm of theproduct of. the weight on the nose wheel and its distance from thereference datum.

At .the'same time wiperarm 121 taps off that portion .of resistance bank113 to place. in circuit resistanceequal,

to the actual moment of the nose wheel divided by 10,000

as illustrated in tabulation VIlI rather than the logarithmic multipleof the moment on resistance 106. Thus, as the moment on the nose wheelis inches times 10,000 pounds, the moment divided by 10,000 will equal100 ohms which is the value of resistance 113 placed in circuit.

The resistance bank 53 and resistance 136 of section B of switch 131which are connected in series from positive main 59 to point 23, formone leg of bridge 104 and the annular resistance bank 107 on thecorresponding panel 34 forms another leg of said bridge. The resistancebank 56 and resistance 136 of section C of switch'131 which areconnected in series from positive main 59 to point 23 form one leg ofbridge 105 and the annular resistance bank 108 on corresponding panel 34forms another leg of said bridge.

As resistance banks 53 and 56 eachhas a value of 4,777 ohms andresistances 136 of sections A and B of switch 131 each has a value of2,634 ohms, the total series resistance of the corresponding legs willeach be 7,411 ohms.

Bridges 104 and 105 will ordinarily be unbalanced and current willtherefore flow through the associated servo-amplifier 26 to energize theservo-motor 31. As a result, the associated drum 33 will rotate untilwiper arms 122 and 124 engage that portion of the associated resistancebanks 107 and 108 respectively to place 7,411 ohms in circuit whenservo-motor 31 is de-energized and drum 33 stops rotating.

At the same time wiper arms 123 and 125, respectively tap off thatportion of resistance banks 114 and 115 respectively, to place incircuit resistance equal to the actual moment of each of the main wheelsdivided by 10,000 as illustrated in tabulation VIII. Thus, as the momenton each main wheel is 430 inches times 30,000 pounds, the moment dividedby 10,000 will equal 1,290 ohms which is the value of each of theresistance banks 114 and 115 placed in circuit.

The resistances 113, 114 and 115 which are connected in series frompositive main 59 to point 23 of bridge 89 form one leg of said bridgeand have a total value of 2,680 ohms. Bridge 89 will ordinarily beunbalanced and current will therefore fiow through the associatedservo-amplifier 26 to energize servo-motor 31. As a result, drum 33 willrotate until wiper arm 101 engages that portion of resistance bank 93 toplace in circuit 2,680 ohms, a multiple of the actual total moment, whenservomotor 31 is tie-energized and drum 33 stops rotating.

At the same time wiper arm 102 will tap ofl that portion of resistancebank 88 to place in circuit resistance equal tothe logarithm times 1,000of the total moments of the weights on the nose wheel and two mainwheels about the reference datum or 1,000,000 plus 12,900,000 plus12,900,000 or 26,800,000. The logarithm of this sum times 1,000 equals7,428 ohms which is the value of resistance bank 88 placed in circuit.

The resistance banks 48, 52 and 55 which are connected in series frompositive main 59 to point 24 of bridge 64 have a total value of 700 ohmsas previously pointed out, and form one. leg of bridge 64. Bridge 64will'be ordinarily unbalanced and current will therefore flow throughthe associated servo-amplifier 26 to energize servo rnotor 31. As aresult, drum 33 will rotate until wiperv arm 74 engages, that. portionof resistance bank 66 to place in circuit 700 ohms, a multiple of theactual total weight; when servo-motor 31 is de-energized drum 33 stopsrotating.

At the same time wiper arm 75 will tap off that portion of resistancebank 68 to place in circuit resistance equal to the logarithm times1,000 of the total weight of 70,000 pounds or 4,845 ohms, which is thevalue of resistance bank 68 placed in circuit.

As resistance bank 68 of bridge 64 and resistance bank 72 of bridge 73are in series and form one leg and resistance bank 88 forms another legof bridge 73, and as the value of resistance 68 has been set to 4,845ohms and that of bank 88 to 7,428 ohms,.as above described, bridge 73will be ordinarily unbalanced. As a result, current will flow throughthe associated servo-amplifier 26 to energize servo-motor 31 and drum 33of bridge 73 will rotate until wiper arm 86 engages that portion ofresistance bank 72 to place in circuit the difference between 7,428 ohmsand 4,845 ohms, i. e., 2,583 ohms. Thus servo-motor 31 is deenergizedand drum 33 stops rotating.

;of said bridge.

- -tate until wiper arm 208 engages Inasmuch ,as the resistance bank 88is of ohmicvalue proportional to the logarithm of the totalmoment andresistance bank 68 is of ohmic value'proportional to the logarithm ofthe total weight, the value of resistance bank 72 in circuit will beproportional to the logarithm of the distance of the center of gravityfrom the reference datum. The anti-logarithm of resistance 72, i. e., of2,583 divided by 1,000 is 383 which is the actual distance from thereference datum of the center of gravity of the aircraft type A loadedas above described. The drum 33 of bridge 73 rotates the pointer P shownin Fig. 7 through transmission 503 to indicate such actual center ofgravity position as 383 inches.

Since CG in percent MAC= 100 the center of gravity determination for thetype A aircraft above illustratively described is converted mto percentMAC as follows:

As the take off center of gravity is within the permissible limits ofthe MAC of the type A aircraft, i. e., between 380 and 400 or between15.2 or 27.4%, the aircraft can take off safely.

During flight of the aircraft, the center of gravity will shift byreason of the reduction of the moment caused by the consumption of fuel.

Assuming that for a given flight the aircraft will consume 500 gallonsor 3,000 pounds of fuel, to determine the landing center of gravity ofthe aircraft, it is merely necessary to turn knob 167 in order to setthe fuel consumption switch 166 to 500 gallons. As a result, the movablearm 165 of switch 166 engages fixed contact 168 associated withresistance 171a and movable arms 201 of sections A and B of switch 202will engage the fixed contacts 203 associated with a resistance 205a ofeach of the two sections A, B respectively.

By reason of the original setting of switch 197 to the type A position,resistance 205a of section A of switch 202 is in circuit, and thecorresponding resistance of section B is inactive. Resistance 205a asindicated in tabulation XIVhas a value of 120.6 ohms for a weight. of3,000 pounds located 402 inches from the nose of the aircraft. a

As resistance bank 95 is identical to resistance bank 93, the associatedwiper arm 99 places in circuit a resistance equal to that of resistancebank 93 placed in circuit by its wiper arm 101, i. e., 2,680 ohms, whichis a multiple of the actual total moment. Resistance bank 95 isconnected at one end to positive main 59 and at its other end to point24 of bridge 98 and forms one leg Resistance bank 193 on panel 34 ofbridge 98 and resistance 205a of section A of switch 202 .are connectedin series between positive main 59 and point 23 of said bridge 98 andform another leg of said bridge. i a

"Bridge 98 will ordinarily be unbalanced and current will flow throughthe associated servo-amplifier 26 to energize servo-rnotor 31. As aresult drum 33 will rothat portion of resistance bank 193 to place incircuit the diiference between 2,680 ohms (resistance bank 95) and 120.6ohms(re- .sistance 205a), i. e., 2,559.4 ohms which is the value ofresistance bank 193 placed in circuit. When this occurs servo-motor 31is deenergized and drum 33 stops rotating.

,. -'At the same time wiper arm 209 of bridge 98 will tap off thatportion of resistance bank 191 equal to the logarithm times 1,000 of theactual remaining moment set by resistance 193, i. e., 7,408 ohms.

The resistance banks 51, 54 and 57 which are connected in series frompositive main 59 to point 23 of bridge 163 have a total value of 700ohms as previously pointed out and form one leg of bridge 163. Theannular resistance 173 on panel 34 of bridge 163 which is connected inseries with resistance 171a of syitch 166 for a fuel consumption of 500gallons or 3,000 pounds, forms another leg of said bridge.

Bridge 163 will be ordinarily unbalanced and current will flow. throughthe associated servo-amplifier 26 to energize servo-motor 31. Drum 33 ofbridge 163 will 22 rotate until wiper arm 1 81 engages that portionof resistance bank 173Ito lace in cir'c it. 670 ohms, 'the'f'diff ferencebetween 700 ohms, the value of resistance banks 51, 54 and 57 and 30ohms, the value of resistance 171a. Thus, servo-motor 31 is de-energizedand drum 33 stops rotating. f v f I At the same time wiper arm 182 willtap off that por tion of resistance bank 175 to place in circuitresistance equal to the logarithm times 1,000 of the weight of 67,000pounds, i. e., the total weight of 70,000 less 3,000 of fuel consumptionweight, or 4,826 ohms, which is the value of resistance bank 175 placedin circuit. A I

As the resistance bank 191, which is connected to point 24 of the bridge179 to formone leg of said bridge, has a value of 7,408 ohms and as theresistance bank 175 has a value of 4,826 ohms and is in serieswith'resistance bank 178 of bridge 179 to form another leg of saidbridge 179, bridge 179 will be ordinarily unbalanced. As a result,current will flow through the associated servoamplifier 26 to energizeservo-motor 31 and drum 33 of bridge 179 will rotate until wiper arm 188engages that portion of resistance 178 to place in circuit 2,582 ohms,the difference between 7,408 and 4,826 ohms. Thus servo-motor 31 isdeenergized and drum 33 stops rotating.

As above described with respect to resistance bank 88, the 2,582 ohms ofresistance bank 178 in circuit is equal to the logarithm times 1,000 ofthe distance of the center of gravity of the aircraft from the referencedatum when 500 gallons of fuel is consumed and the antilogarithm ofresistance 178, i. e. of 2,582 divided by 1,000 is 382, which is thelanding center of gravity of the type A aircraft based on a fuelconsumption of 500 gallons or 3,000 pounds. Thus, the center of gravityhas moved forward one inch. 7

The operation of the embodiment of Fig. 3 in which the main wheels ofthe aircraft are selected as the reference datum will now be describedin connectionwith type A aircraft of the same specifications and loadingused in the foregoing description.

With the aircraft set upon the scales 245, 246 and 247, the aircraftselector switches 287 and 349 are set-to type A position by turning knob291. This will also set the switch 322 to the type A position shown. Asa result, the movable arms 289 and 348 of switch 287 and 349 will engagethe fixed contact 288 associated with the resistances 292a and 292arespectively and the movable arm 321 of switch 322 will engage the fixedcontact 323 associated with the type A position. ,The weight on scale245 being 10,000 pounds and the weights on each of the'scales 246 and247 being 30,000 pounds, the movable arms 249 and 251 controlled by thenose scale 245 will tap oif that portion of the associated resistancebanks 255 and 256 of ohmic value equal to the logarithm of the weightmultiplied by 1,000as il1ustratively shown in tabulation III. Thus, thevalue of 02111011 resistance bank 255, 256 in circuit will be 4,000 0ms.

Simultaneously, the movable arms 248, 252 and 253 of the weighing scaleswill tap off that portion of the resistance banks 254, 257 and 258respectively of ohmic value equal to the actual weight divided by asillustrated in tabulation IV. Thus the value of the resistance banks254, 257 and 258 in circuit will be 100, 300 and 300 ohms or a total of700 ohms.

The resistances 292a and 292'a placed in circuit are of ohmic valueequal to the logarithm multiplied by 1,000 of the distance between thenose wheel center and the main wheel centers along the longitudinal axisof theaircraft, as illustrated by tabulation VI. Such distance beingequal to 330 inches, the value or each resistance 292a and 292a is 2,519ohms.

As a result of the initial setting of the equipmentito the type Aposition, the resistance banks 254, 257 and 258 in series (700 ohms)will constitute one leg of the Wheatstone bridge 265. As the resistance267 on panel 244 forms another leg of bridge 265, the bridge 265 will beordinarily unbalanced and current will flow through the associatedservo-amplifier 236 ,to energize servomotor 241. As a result, theassociated drum 243 will rotate until wiper arm 282 taps off thatportion of resistance 267 equal to 700 ohms when servo-motor 241 isde-energized and drum 243 stops rotating. 1

- At the same time wiper arm 281 taps off that portion of resistance 269to place resistancein circuit equal to g the logarithm times 1 ,000 ofthe total weight. Theloga- 23 rithm times 1,000, of? this 5, sum,equals, 4,845 which is .the value of resistance 26 9.placcd in circuit.

The, resistance bank 25 5; (4,000 ohms) andresistance 292a (2,519 ohms)of; switch 287 which are. connected in series from positive main 261 topoint 234 of bridge 276, form one, leg of saidbridge andhavea totalvalue of 6,519 .ohms and1he resistances269 and275 which are alsoconnected in seriesform another legof bridge, 276.

As the value of.- resistance bank 269Lhas been set to 4,845; ohms, asabove described, bridge2176 will beordinarily unbalanced., As .aresult,current will flow through the, associated servo-amplifier 236 to.energize servo motor 241 and drum 243 of ,bridge 276 .will rotateuntilwiperarm 2 94. engages thatporti'on of resistance bank 275 .to placein..circ1 1;it.1,674 chins, the difference between 6,519 and 4,845 ohms.Atthistime servo-motor, 241 is lde-energized and ,drum '243 stopsrotating.

Inasmuchas the-sum of resistance banks 255 and 292a is of ohmic valueproportional' to the logarithm of the moment of thenose Wheel withrespect to the main wheels aridresistance hank269is of ohmic valueproportional to the-logarithm of;the;totalyweight, the. value of theresistancefbank 275j,will;be. equal to the logarithm times 1,000 ofthedistance of thecenter of, gravity from the centers; ofthemain wheels.The antilogarithm-of 11674 or'47.2i is therefore the 'distance from themain wheels of the center of gravity, of the, aircraft. type A loaded asabove'described. That distance'may be read on a suitableanti-logarithmic scale; on drum 243.

This centerof gravity may be related to a percent of the MAC by theformula:

. H'Y CG 1n percent MAO=,. 100,

As this take-off center of gravity. iswithin the permissiblelimits ofthe MAC of the type A aircraft, i. e. between 380 and 400 inches fromthe nose or between 30 and. 50 inches from the main Wheels, or between15.2% and 27.4%' MAC the aircraft will take off safely.

Thus, the single, moment system of Fig. 3 gives the same center ofgravity and of percent MAC readings as the; three moment system of,Figs. 1 and 2. it will not be necessary. to show the like equivalencywith respect to fuel consumption.

The-embodiment ofEig. 4 differs from that of Fig. 3 tin affording. fourweighing scales, the aircraft being mountedon those three of theweighing scales which would position it;transversely. of the wind andthus avoid deviation from correct reading of the actual weight, all .asaboveset forth. With the" nose wheel, say on scale 361 -and the two mainwheels on scales 362 and-.464, the aircraft; selector switch 431 is settottypeA position so that movable arm 429 will engage the fixed contact;432 connected to resistance 433.

The weightof-thexaircraft on scales 361, 362 and 364 closes the:respective micro-switches 437, 438and 441,

CG in percent; MAC: X 100: 16.9%

completing circuits-frompositive main 394 to the coils 455,.456-and 458,respectively. As a result, movablearm 4650f relay 459 .will' engagefixed contact 464; movable arms 468 and 469 of relay 461 will engagefixed contacts 4,66 and 467 respectively and movable arms 431, 482*and483 of relay 463 will engage fixed contacts 477, '47 8t and -47 9respectively.

A circuitis thus completed from positive main 394, closed contacts 464,465, lead 484, closed contacts 466, 46 8, lead 486,. closed contacts477, 48.1, lead 494 to one side of coil 497 of relay 419 and from theother side of coil'497 to negative main 366. As only coil 497 ofrelay419Wlll be energized, the contacts 415, 424 thereof will close tocomplete a circuit from movable arm 376 of weighingscale 361 to movablearm 4290f selector switch- 431.

The weight on scale 361 being 10,000 pounds, the movable-arm376-controlled by scale 361 will tap off that portion of the resistancebank 385 which is of ohmic value equal to the logarithm times 1,000ofthe weight as illustratively shown in tabulation III; Thus, the valueof resistance bank. 385 in circuit is4,000 ohms.

Simultaneously. the movable. arms-377, 379'and 384 of of ohmic valueequal to the actual Weight (i. e. 10,000,

24 30,000 and 30,000 pounds respectively) divided by as illustrated intabulation 1V. Thusthe value of resistance banks 389, 391 and 393 incircuit will belOO, 300 and 300 ohms. As noweight is onscale 363,, themovable arm 382 of the latter will tap off no resistance from resistancebank,392.

The resistance 433 placed in circuit by the setting of aircraft selectorswitch 431 is of ohmic value equal to the logarithm times 1,000 of thedistance of the nosewheel centerv from that of the main wheels asillustrated by tabulation VI. As such distance is 330 inches, the valueof resistance 433 is 2,519 ohms.

The series connected resistance banks 389, 391 and 393 have a value of700 ohms and form one leg of bridge 399. The bridge 399 will beordinarily unbalanced and current will flow through the associatedservo-amplifier 367 to energize servo-motor 372. As a result, theassociated drum 374 will rotate until wiper arm 409 taps off thatportion of resistance bank 402 equal to 700 ohms, when the bridge 399will be in balance andservo-motor 372 Will be deenergized so that drum374 will stop rotating.

Atthe same time the wiper arm 411 willtap offthat portion of resistancebank 404 to place resistance in circuit equal to -the logarithm times1,000 of the total weight as illustrated by tabulation X11. As the totalweight is-70,000 pounds, the logarithm times 1,000 of this sum equals4,845 which is the value of resistance bank 404 placed in circuit.

The resistance bank 385 (4,000 ohms) and resistance 433 (2,519 ohms) areconnected in series from positive main 394 to point 364 of bridge 408asa total resistance of 6,519 ohms. As the value of resistance bank 404has been set to 4,845 ohms, as above described, bridge 408 will beordinarily unbalanced. As a result, current will flow throughservo-amplifier 367 to energize servo-motor 372 and drum 374 of bridge408 will rotate until Wiper arm 414 engages that portion of resistance407 to place in circuit 1,674 ohms, the difference between 6,519 and4,845 ohms. At this time servo-motor 372is deenergized and drum 374stops rotating.

Inasmuch as the sum of resistance bank 305 and resistance 433 is ofohmic value proportional to the logarithm of the moment of the nosewheel with respectto the main wheels, and resistance hank 40-4 is ofohmic value proportional to the logarithm of the total weight, the valueof resistance bank 407 will be equal to the logarithm times 1,000 of thedistance of the center of gravity from the centers of the main wheels.The antilogarithm of 1.674 or 47.2 is therefore the distance from themain wheels of. the center of gravity of the type A aircraft loaded asabove described. Thatdistance may be readon a suitable anti-logarithmicscale on drum 374.

Should the wind be from another direction, the aircraft mightillustratively be positioned with the nose wheel on scale 362 and thetwo main wheels on scales 361 and 363.

As a result, the micro-switches 437, 438 and 439. will be closed toenergize coils 455, 456 and 457 of relays 459, 461 and 462. A circuitwill be comnleted'from positive main 394, closed contacts 464 and 465 ofrelay 459, lead 484, closed contacts466, 468 of relay 461, lead 487,closed contacts 471, 474 of relay 462, lead 489. to coil 491 of relay421. Asa result, the resistance bank 386, which has a value of 4.000ohms will be connected in series with resistance 433 of selector switch431 and the equipment will thereupon operateas previously described.

If depending upon the direction of. the wind the nose wheel is placed onany of the four scales, the correct center of gravity or percent MACwould be indicated with the substantial elimination of any divergenceotherwise incurred due to the force of the wind.

It will be understoodthat the arrangement shown in Fig. 4 foreliminating divergence in the actual reading of the weighing scales dueto the wind, would desirably be incorporated in the system. shown inFigs. 1 and 2 as well as in the otherwise complete system shown in Fig.3, only part of which has been shown in the diagrammatic view of Fi 4.

Ordinarily the single moment system of Fig. 3 will serve for aircraftgenerally of familiar design when. loaded according to present daypractice. However, other types of aircraft under consideration. atpresent or in the future, or. systems ofloading not at presentconventional, may

" render desirable the more complex three moment system '25 of Figs. 1and 2 and this may conceivably be extended, on the principle wellunderstood from the foregoing description, to aircraft that may havefour or more wheels.

"lhe invention may be carried into practice according to either of twogeneral procedures: (a) to check the center of gravity position of theaircraft immediately prior to take otf, and (b) to check the center ofgravity position as the aircraft is being loaded.

In the first of these procedures, the aircraft would be loaded accordingto conventional practice but would be taxied to the weighing scales andpositioned thereon at right angles to the direction of the wind,affording an immediate reading preferably indicated in the control toweror, if desired, on the field as well. If the indication shows that thecenter of gravity is within the safe range of position or within thesafe range of per cent MAC, the aircraft would be cleared for takeoffwith assurance that there are no fortuitous divergences.

The effect of fuel consumption on the center of gravity position woulddesirably also be checked at this time to assure that the center ofgravity is within safe limits for landing at the destination. To thisend the fuel consumption switch would be turned to the estimated fuelconsumption for the projected flight and the center of gravity orpercent MAC would immediately be read to assure that it remains withinthe safe limits.

it is of course to be understood that instead of or in addition toproviding the circuits herein described for determining the effect offuel consumption on the position of the center of gravity, an identicalcircuit or circuits could be. used to determine the effect of thedropping of cargo or personnel such as lire lighters or the like fromthe aircraft while it is in flight.

Should the center of gravity or percent MAC indication be outside of thesafe range for either flying or landing, the aircraft would be refusedclearance and appropriate ad ustments in the loading would be made untilthe indication registers complete safety both for flight and forlanding.

The need for readjustment would of course be minimized if the secondprocedure were followed and the aircraft were positioned upon theweighing scales throughout the loading operation, so that the center ofgravity could be observed on the indicator as the loading proceeds, butparticularly toward the completion of the loading at which stage theloading would be controlled in order that the center of gravity isobserved to be within safe limits and the need for redistributing theload would be dispensed with.

It is of course to be understood that although the aircraft selectorswitches permit aircraft of different types to' be measured, such switchcould be eliminated if the equipment is to measure but one type ofaircraft as the distance from the wheels to the reference datum would bepredetermined.

While the Wheatstone bridge principle is shown in the drawings and fullydescribed in the specification, it will be understood that thisexpedient is largely illustrative of means generally for opposingunbalanced impulses and automatically causing such unbalance to bringabout desired balance.

- While in the specification and the drawings only re- :sistances havebeen shown as the electrical regulating means, it is of courseunderstood that impedances could be used for the purpose and 1t is alsounderstood that whether in the Wheatstone bridge type of arrangement orin other arrangements for opposing the initially unbalanced impulses,there could be used systems of electronic oscillators that operate theautomatic adjusting motor by differences in frequencies and bring anadjustable oscillator to the frequency of an oscillator that is set bythe parameter being measured or by the impulse applied. The frequency ofthe two oscillators in opposition will be determined by a variableimpedance, including inductance and capacitance, in which preferably thecapacitance element is adjusted at one side of the balancing unit toattain the controlling frequency of its associated oscillator while themotor controlled by the differences of frequency automatically adjuststhe capacitance in the other side of the balancing unit until thefrequencies of both sides are equal.

In the broader claims it will be understood that the reference toimpulses is meant to include not only currents through resistances, butalso currents from electronic ,oscillators in which latter case theoutput frequencies will be combined to produce a resultant differencefrequency.

The expedient of the opposing currents and morepaifticularly theWheatstone bridge instrumentalities fi i'f translating given resistanceinto logarithmic valueslfor multiplication or division as the case maybe, hasjparticu lar utility as above set forth in the particularrelation described. It will be understood of course that each of theself-balancing Wheatstone bridges could be utilized from the broadestaspect of the invention, in obtaining an ultimate measurement of productor quotient made up of any of a wide variety of parameters other thanweight or distance.

Thus, the variable resistance will equal the product of one of thelogarithmic resistances by a first power ofthe second logarithmicresistance, that power being positive when both logarithmic resistancesare opposed to the variable resistance and being negative where only thefirst resistance is so opposed and the second resistance is in serieswith the variable resistance. r

Should it be desired for any purpose to read the value of a moment, apointer moving about an .ap: propriate scale need merely be driven froma servomotor that sets variable resistance opposed to series connectedresistances of distance and weight, which determine moment. Similarly,weight could be read directly from variable resistance opposed to weightresistance.

As many changes could be made in the above method and apparatus, andmany apparently widely different embodiments of this invention could bemade without departing from the scope of the claims, it is intended thatall matter contained in the above description or shown in theaccompanying drawings shall be interpreted as illustrative and not in alimiting sense.

Having thus described my invention, what I claim as new and desire tosecure by Letters Patent of the United States is:

1. Equipment comprising two variable impedance unit calibratedrespectively in proportion to the actual and to the logarithmic valueof, a parameter to be measured, a third impedance unit of calibrationcorresponding to that of one of the two impedance units, means forsetting said third impedance unit to a value corresponding to suchparameter, means for connecting a power supply for opposed current flowthrough said third impedance unit and the corresponding one of saidother two impedance units, means in driving relation to said twovariable impedance units and actuated by the resultant difference ofpotential, whereby actuation of said means will elfect variation of saidtwo variable impedance units until the impedance units connected foropposed -current flow have the same value, and means .under control ofthe other of ,said two ,variable impedsaid third impedance unit to avalue corresponding to such parameter, means for connecting a powersupply for opposed current flow through the two impedance units that arecalibrated in proportion to the actual value of such parameter, drivingmeans for said two variable impedance units actuated by the resultantdifference of potential, whereby actuation of said driving means willeffect variation of said two variable impedance units until theimpedance units calibrated in proportion to actual value have the samevalue, and means under control of the variable impedance unit calibratedin proportion to logarithmic value for effecting an indication of whichthe parameter is a factor.

4. Equipment comprising two variable impedance units calibratedrespectively in proportion to the actual and to the logarithmic value ofa parameter to be measured, a third impedance unit calibrated inproportion to the logarithmic value of such parameter, means for settingsaid third impedance unit to a value corresponding to such parameter,means for connecting a power supply for opposed current flow through thetwo impedance units that are calibrated in proportion to the logarithmicvalue of such parameter, driving means for said two variable impedanceunits actuated by the resultant difference of potential, wherebyactuation of said driving means will 27 efiect variation ofsaidtwovariableiimpedance.units until the impedance unitsflalibrated inproportion to logarithrn'iclvalue have the same Value, and means undercontrol'of the variable impedance unit calibrated in proportion toactual value for effecting an indication of which the parameter is afactor.

5. Equipment comprising a variable resistance unit calibrated to ohmicvalues proportional to the actual value of a parameter to be measured,twoganged variable' resistance units calibrated respectively to ohmicvalues proportional to the actual and to the logarithmic value of suchparameter, means for connecting a power supply. for opposed current flowthrough said two resistanceunits thatare calibrated in proportion to theactual value of the parameter, an electric motor connected with respectthereto to be driven by the resultant difference of potential and indriving relation to said two ganged variableresistance units, wherebyoperation of the motor will effect adjustment of the resistance unit ofthe ganged units calibrated in proportion to the actual value of theparameter until it equals the ohmic value of said variable resistanceunit, at which time the difference of potential is eliminated and themotor stops operating, said logarithmically calibrated resistance unitbeing thus set to a value proportional to the logarithm of suchparameter.

6. Equipment for determining the distance of the center of gravity froma given reference datum of an aircraft of the type'having two mainwheels and a third wheel, comprising means to place in circuit impedanceof value proportional to the logarithm of total moment with respect tosuch given reference datum, variable impedance units associated with therespective wheels, each calibrated in proportion to the actual weightcarried, means additively connecting said variable impedance units for acombined impedance proportional to the actual weight of the aircraft, anadditional impedance unit calibrated logarithmically, and meanscontrolled by such weight governed additively connected impedances toplace into circuit such portion of the additional impedance unit as isof value proportional to the logarithm of the actual total weight of theaircraft, a variable impedance additively connected with respect to saidweight impedance, and calibrated logarithmically, and means to passopposing currents from a common source through said impedance of valueproportional to the logarithm of total moment and the additivelyconnected logarithmically calibrated impedances, means controlled by theresultant difference of potential to adjust said variable impedanceuntil the difference of potential is eliminated, at which time the valueof the variable impedance is equal to the difference between those ofthe other logarithmically calibrated impedances, and an indicatorcorrelated with said variable impedance affording an anti-logarithmicreading proportional to said difference of impedances and designatingthe position of the center of gravity of the aircraft with respect tosuch given reference datum.

7. The combination set forth in claim 6 in which three weighing scalesare provided to support. the respective wheels of an aircraft and inwhich the weight of the aircraft on the scales serves to place incircuit the impedances proportional to the respective weights.

8. The combination set forth in claim 6 in which the following meansserves to determine the logarithm of total moment of. an aircraft, avariable impedance unit calibrated to values proportional to thelogarithm of weight on such third wheel, and an impedance unitadditively connected to said third wheel variable impedance unit andcalibrated to value proportional to the logarithm of distance from thereference datum of such aircraft to the third wheel.

9. The combination set forth in claim 6 in which the impedanceproportional to the logarithm of the total moment is obtained by threeweighing scales to support the main wheels and third wheel of anaircraft respectiveiy and in which three pairs of impedances areassociated respectively with each of such scales, one of the impedancesof each pair. being calibratedto values proportional to the logarithm ofweight on the associated wheel and the other impedance of'each pairbeing calibrated to a value proportional to the logarithm of thedistance of the associated wheel from the reference datum, each of-saidpairs of impedances being additively connected for a combined'impedancevalue proportional to the logarithm of-the product of the weight on theassociated wheel and its distance from thereferen'ce datum, means-tomeasure off-by said respective pairs of impedances, impedances which arerespectively proportional to' the respective products, meansadditivelyco'nnecting said respective product impedances, and means tomeasure off by said latter additively connected impedances, the desiredimpedance of value which is proportional to the logarithm of thecorresponding sum of the products.

10'. The combination in which the final means recited in claim 9comprises a duplex variable impedance unit one element being calibratedto a value proportional to the actual value of the sum of saidadditively connected product impedance and the other element beingcalibrated to values proportional to the logarithm of'said sum.

11. The combination set forth in claim 6 in which the center of gravityindicationhas a minimum, a maximum and a mean value for the smallesttype aircraft to be measured and a multiplier impedance is additivelyconnected to said variable impedance and of value proportional to theditference between the'logarithrns of the mean value of the centerofgravity for the smallest and the largest type aircraft to be measured.

12. The combination set forth in claim 6 which includes four weighingscalesany three of which may carry respectively the two main wheels andthe third wheel of an aircraft, an impedance unit'associated with eachof said four scales, said impedance units being calibrated respectivelytovalues proportional to the logarithm of the weight on the associatedscale, an impedance unit calibrated to values proportional to thelogarithm ofthe' distance from the third wheel'to the main wheels,switch means controlled by the weight due to the three wheels of theaircraft on the associated three scales additively to connect theimpedance unit which is associatedwith the weight on the third wheelwith said distance impedance unit, said additively connected distanceimpedance unit and weight impedance unit constituting the impedancemeans of value proportional to the logarithm of the total moment. i

13. The combination recited in claim 6 in whichthere are additionalfacilities to ascertain the changed position of the center of gravityupon withdrawal of weight from any given position on the loadedaircraft, said additional facilities comprising a manually set devicedetermining the moment with respect to the reference datum of the Weightremoved, a second manually set device determining the weight removed,impedances under control of said respective devices, means to opposesaid impedances respectively to impedances equal to the total momentimpedance and the total weight impedance, variable impedances additivelyconnected respectively with the set moment impedance and the'set weightimpedance, impedances of logarithmic value corresponding to those of therespective variable impedances, means under control of the respectivevariable impedances for measuring oif from said logarithmic impedancesimpedances proportional respectively to the logarithm of the adjustedmoment and-to the logarithm of the adjusted weight, a variable impedanceadditively connected to said measured off logarithmic weight impedance,means opposing current from. a common source through saidmeasured offlogarithmic moment impedance and said additively connected impedances,means controlled by the resultant difference of potential to adjust saidlast named variable impedance until the difference of potential iseliminated at which time the value of said variable impedance is equalto the difference between the measured off logarithmic impedances and anindicator correlated with said variable impedance which is calibrated inproportion to the anti-logarithm'of-said difference of impedances andhence designates the position of the adjusted center of gravity of theaircraftwith respect to the reference datum.

14. Equipment for determining the distance from a given reference datum,of the center of gravity of an aircraft having two main wheels and athird wheel which comprises three variable impedance units calibratedlinearly and adapted to be set" to values proportional to actual weightsto be carried'by the respective wheels, said units being connected foraddition of their impedances, two variable impedance units, the first ofthe two units being calibrated linearly and adapted to be set to valueproportional to such added impedances and'the other unitbeing'calibrated to'value's proportional to the logarithm of suchaddeddmpedance's, means for connecting a power supply for opposedcurrent flow through said additively connected impedance units and thefirst of said two variable impedance units, means in driving relation tosaid two variable impedance units and actuated by the resultantdifference of potential, whereby actuation of said means will effectvariation of said two variable impedance units until the first of saidtwo variable impedance units has the same value as said additivelyconnected impedance units, the other of the two impedance units beingthereby set to a value proportional to the logarithm of the total weightof the aircraft, a variable impedance unit logarithmically calibratedand adapted to be set to values proportional to the logarithm of weightcarried on such third wheel, an impedance unit logarithmicallycalibrated and additively connected to said third wheel variableimpedance unit and adapted to be set to value proportional to thelogarithm of the distance from the reference datum of such aircraft tothe third wheel, said two additively connected impedance units having acombined value proportional to the logarithm of the moment of the weighton the third wheel with respect to such reference datum, a variableimpedance unit calibrated logarithmically and additively connected tosaid logarithmic total weight impedance unit, means to pass opposingcurrents from a common source through said additively connectedimpedance units related to moment, and said additively connectedlogarithmic total weight impedance unit and variable impedance unit,means controlled by the resultant difierence of potential to adjust saidvariable impedance unit until the difierence of potential is eliminated,at which time it has a value equal to the difference between the momentimpedance and total weight impedance, and an indicator correlated withsaid variable impedance unit which is calibrated in proportion to theanti-logarithm of said difference of impedances and hence designates theposition of the center of gravity of the aircraft with respect to suchreference datum.

15. The combination set forth in claim 8 in which the distanceresistance is adapted to be manually set for the particular type ofaircraft to be measured.

16. Equipment for determining the position with respect to a givenreference datum of the center of gravity of an aircraft of the type thathas a plurality of supporting gear, said equipment comprising anadjustable variable impedance means for each of said supporting gear,

.means to set each adjustable variable impedance means to a value thatcorresponds to the weight on the associated supporting gear, a furtherimpedance means for each supporting gear, and of value that correspondsto the distance of the associated supporting gear from the referencedatum, a plurality of bridge circuits corresponding in number to thenumber of supporting gear, each of said bridge circuits having abalancing impedance means, said balancing impedance means and saidadjustable impedance means being in difierent arms of said bridgecircuit and said further impedance means and said balancing impedancemeans being in different arms of said bridge circuit, whereby thebalancing of each of said bridge circuits efiects setting of saidassociated balancing impedance means to a value that corresponds to theproduct of the weight on and the distance of the associated supportinggear from the reference datum, which therefore corresponds to the momentwith respect to said reference datum of the weight on the associatedgear, a second additional impedance means also controlled by each ofsaid bridge circuits to be set to a value proportional to the associatedmoment, a further bridge circuit, means additively connecting saidsecond additional impedance means for a total impedance valueproportional to the total moment of the weights with respect to saidreference datum, on all of said supporting gear, means connecting in onearm of said further bridge circuit impedance means of value proportionalto said total moment, a total weight impedance means in a second arm ofsaid bridge, means to set said total weight impedance means to a valuethat corresponds to the total weight of the aircraft, and a balancingimpedance means, said total moment impedance means and said total weightimpedance means being in difierent arms of said further bridge circuit,said balancing impedance means and said total moment impedance meansbeing in difierent arms of said further bridge circuit, whereby thebalancing of said further bridge circuit efiects setting of saidbalancing impedance means to a value that corresponds to the distance ofthe center of gravity from the reference datum.

References Cited in the file of this patent or the original patentUNITED STATES PATENTS 1,573,850 Naiman Feb. 23, 1926 2,108,146 SimpsonFeb. 15, 1938 2,373,504 Schlieben et al. Apr. 10, 1945 2,443,045Magruder et al. June 8, 1948 2,443,098 Dean June 8, 1948 2,520,428Nilabanton Aug. 29, 1950 2,540,807 Berry Feb. 6, 1951 2,541,429 Mathes,Ir., et a1. Feb. 13, 1951 2,559,718 Goodlett et al. July 10, 19512,615,330 Blackman et al. Oct. 28, 1952 FOREIGN PATENTS 625,023 GreatBritain June 21, 1949 OTHER REFERENCES Electronic Instruments; Greenwoodet al., Figure 6.7(b); page 139; McGraw-Hill, 1948.

Bridge Type Electrical Computers; W. E. Ergen', The Review of ScientificInstruments"; volume 18, No. 8; August 1947; pages 564-567.

